Sublinear singular elliptic problems with two parameters

We establish several existence and nonexistence results for the boundary value problem <f>−Δu+K(x)g(u)=λf(x,u)+μh(x)</f> in <f>Ω</f>, <f>u=0</f> on <f>∂Ω</f>, where <f>Ω</f> is a smooth bounded domain in <f>RN</f>, <f>λ</f> and <f>μ</f> are positive parameters, <f>h</f> is a positive function, while <f>f</f> has a sublinear growth. The main feature of this paper is that the nonlinearity <f>g</f> is assumed to be unbounded around the origin. Our analysis shows the importance of the role played by the decay rate of <f>g</f> combined with the signs of the extremal values of the potential <f>K(x)</f> on <f>Ω¯</f>. The proofs are based on various techniques related to the maximum principle for elliptic equations. [Copyright &y& Elsevier]